| Title:
|
Fixed point theorems for nonexpansive operators with dissipative perturbations in cones (English) |
| Author:
|
Chang, S. S. |
| Author:
|
Chen, Y. Q. |
| Author:
|
Cho, Y. J. |
| Author:
|
Lee, B. S. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
39 |
| Issue:
|
1 |
| Year:
|
1998 |
| Pages:
|
49-54 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $P$ be a cone in a Hilbert space $H$, $A: P\rightarrow 2^P$ be an accretive mapping (equivalently, $-A$ be a dissipative mapping) and $T:P\rightarrow P$ be a nonexpansive mapping. In this paper, some fixed point theorems for mappings of the type $-A+T$ are established. As an application, we utilize the results presented in this paper to study the existence problem of solutions for some kind of nonlinear integral equations in $L^2(\Omega)$. (English) |
| Keyword:
|
nonexpansive mapping |
| Keyword:
|
accretive mapping |
| Keyword:
|
fixed point theorem |
| Keyword:
|
nonlinear integral equations |
| MSC:
|
45G10 |
| MSC:
|
45H10 |
| MSC:
|
47H06 |
| MSC:
|
47H09 |
| MSC:
|
47H10 |
| MSC:
|
47H15 |
| idZBL:
|
Zbl 0937.47053 |
| idMR:
|
MR1622324 |
| . |
| Date available:
|
2009-01-08T18:38:44Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118983 |
| . |
| Reference:
|
[1] Alspach D.E.: A fixed point free nonexpansive map.Proc. Amer. Math. Soc. 82 (1981), 423-424. Zbl 0468.47036, MR 0612733 |
| Reference:
|
[2] F. E. Browder F.E.: Nonlinear nonexpansive operators in Banach spaces.Proc. Nat. Acad. Sci. U.S.A 54 (1965), 1041-1044. MR 0187120 |
| Reference:
|
[3] Browder F.E.: Nonlinear Operators and Nonlinear Equations of Evolution in Banach Spaces.Proc. Symp. Pure Math. Vol. 18, Part 2 (1976). Zbl 0327.47022, MR 0405188 |
| Reference:
|
[4] Chang S.S.: Fixed Point Theory with Applications.Chongqing Publishing House, Chongqing (1984). |
| Reference:
|
[5] Chen Y.Q.: The fixed point index for accretive mappings with $k$-set contraction perturbation in cones.Internat. J. Math. and Math. Sci. 2 (1996), 287-290. MR 1375990 |
| Reference:
|
[6] Chen Y.Q.: On accretive operators in cones of Banach spaces.Nonlinear Anal. TMA 27 (1996), 1125-1135. Zbl 0883.47057, MR 1407451 |
| Reference:
|
[7] Chen Y.Q., Cho Y.J.: On $1$-set contraction perturbations of accretive operators in cones of Banach spaces.J. Math. Anal. Appl. 201 (1996), 966-980. Zbl 0864.47027, MR 1400574 |
| Reference:
|
[8] Gatica J.A., Kirk W.A.: Fixed point theorems for contraction mappings with applications to nonexpansive and pseudo-contractive mappings.Rocky Mountain J. Math. 4 (1994), 69-79. MR 0331136 |
| Reference:
|
[9] Isac G.: On an Altman type fixed point theorem on convex cones.Rocky Mountain J. Math. 2 (1995), 701-714. Zbl 0868.47035, MR 1336557 |
| Reference:
|
[10] Kirk W.A., Schonberg R.: Some results on pseudo-contractive mappings.Pacific J. Math. 71 (1977), 89-100. MR 0487615 |
| Reference:
|
[11] Morales C.: Pseudo-contractive mappings and the Leray-Schauder boundary condition.Comment. Math. Univ. Carolinae 20 (1979), 745-756. Zbl 0429.47021, MR 0555187 |
| Reference:
|
[12] Reinermann J., Schonberg R.: Some results and problems in the fixed point theory for nonexpansive and pseudo-contractive mappings in Hilbert spaces.Academic Press, S. Swaminathan ed. (1976). |
| . |
